1. What is Machine Learning

Machine Learning is a branch of Artificial Intelligence the enables computer systems to learn from observation just the way humans learn without being explicitly programmed.. In machine learning, the system is presented with a set of data or objects. This is called the training set. The goal is for the system to examine this data and learn the attributes. This process is called training. After the training process, the system is able to classify when new input is provided.
For example, your camera is able to detect faces because it has been trained to recognize a face based on the features.
Machine Learning is divided in Supervised Learning and Unsupervised Learning. This is clearly explained in Introduction to Machine Learning and What is Machine Learning video tutorial.

2. Limitations of Machine Learning

Machine Learning has some of the following problem

Managing high-dimensional data. This means that conventional machine learning model does not perform well when there is very large input and output dataset.

Does not handle feature extraction efficiently. Features have to be manually provided and used to train the data.

Machine Learning is a subset of AI and Deep Learning is a subset of Machine Learning

3. What is Deep Learning

Machine Learning is a subset of AI and Deep Learning is a subset of Machine Learning

Deep learning tends to build learning algorithms that mimic the way the human brain process information. Deep learning is implemented by means of neural networks. The key is that for a neural network to be used to efficiently model deep learning algorithms, then it must consist of a several hidden layers.
This is where the name 'deep learning' comes from. The input passes through many layers ( like goes deep). And then the output is passed back into the input repeatedly until the best output is produced. This process could be either back-propagation or gradient descent